> In addition to all the sensible reasons others have pointed out, if you crash at a high enough speed without a seatbelt you become a projectile.

This pales in comparison to the projectile that your care already is.

In any case, just work out the expected level of danger, convert to monetary units, and tax people who don't wear seatbelts.

> If the seatbelt saves your life from an accident in which you were at fault, it is easier to prosecute and extract compensation from the living than from the dead.

Tax non-seatbelt-wearers ahead of time. Or make sure everyone has insurance, get the money from the insurance, and beancounters at the insurace will make sure premiums go up for non-seatbelt-wearers. (And use the full force of the law against people without insurance. Or have some clever mechanism design, like selling default insurance with petrol, but give people with proven insurance a discount on that, etc.)